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Beliebt Rechnen >

(\partial)/(\partial x)(x^{x^2-y^2})

Lösung

\frac{\partial}{\partial x} (x^{x^{2} - y^{2}})

Lösung

x^{x^{2} - y^{2}} (2 x ln (x) + \frac{x ^{2} - y ^{2}}{x})

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{x^{2} - y^{2}})

Behandle

y

als Konstante

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{x^{2} - y^{2}} = e^{(x^{2} - y^{2}) l n (x)}

= \frac{\partial}{\partial x} (e^{(x^{2} - y^{2}) l n (x)})

Wende die Kettenregel an:

e^{(x^{2} - y^{2}) l n (x)} \frac{\partial}{\partial x} ((x^{2} - y^{2}) ln (x))

= e^{(x^{2} - y^{2}) l n (x)} \frac{\partial}{\partial x} ((x^{2} - y^{2}) ln (x))

\frac{\partial}{\partial x} ((x^{2} - y^{2}) ln (x)) = 2 x ln (x) + \frac{x ^{2} - y ^{2}}{x}

= e^{(x^{2} - y^{2}) l n (x)} (2 x ln (x) + \frac{x ^{2} - y ^{2}}{x})

e^{(x^{2} - y^{2}) l n (x)} = x^{x^{2} - y^{2}}

= x^{x^{2} - y^{2}} (2 x ln (x) + \frac{x ^{2} - y ^{2}}{x})

Beliebte Beispiele

derivative of ((-2x^2+2x)/((3x-3)))

\frac{d}{d x} (\frac{( - 2 x ^{2} + 2 x )}{( 3 x - 3 )})

derivative of (40/(3x^{1/3)})

\frac{d}{d x} (\frac{40}{3 x ^{\frac{1}{3}}})

limit as x approaches 0 of (sqrt(x+4)-2)/(sin(5x))

x \to 0 lim (\frac{x + 4 - 2}{sin ( 5 x )})

integral of 39arctan(sqrt(x))

\int 39 arctan (x) d x

integral of 6tsin(t)

\int 6 t sin (t) d t